Preprints
https://doi.org/10.5194/gmd-2023-78
https://doi.org/10.5194/gmd-2023-78
Submitted as: development and technical paper
 | 
25 May 2023
Submitted as: development and technical paper |  | 25 May 2023
Status: this preprint is currently under review for the journal GMD.

An improved version of the Piecewise Parabolic Method advection scheme: description and performance assessment in a bidimensional testcase with stiff chemistry in toyCTM v1.0

Sylvain Mailler, Romain Pennel, Laurent Menut, and Arineh Cholakian

Abstract. This study displays a novel method to estimate the performance of advection schemes in numerical experiments along with a semi-realistic non-linear, stiff chemical system. This method is based on the examination of the "signature function", an invariant of the advection equation. Apart from exposing this concept in a particular numerical testcase, we show that a new numerical scheme based on a combination of the Piecewise Parabolic Method (PPM) with the flux adjustments of Walcek outperforms both the PPM and the Walcek schemes, for inert tracer advection as well as for advection of chemically active species. From a fundamental point of view, we think that our evaluation method, based on the invariance of the signature function under the effect of advection, offers a new way to evaluate objectively the performance of advection schemes in the presence of active chemistry. More immediately, we show that the new PPM+W ("Piecewise Parabolic Method + Walcek") advection scheme offers chemistry-transport modellers an alternative, high-performance scheme designed for Cartesian-grid Eulerian Chemistry-transport models, with improved performance over the classical PPM scheme. The computational cost of PPM+W is not higher than that of PPM. With improved accuracy and controlled computational cost, this new scheme may find applications in other fields such as ocean models or atmospheric circulation models.

Sylvain Mailler et al.

Status: open (until 20 Jul 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse

Sylvain Mailler et al.

Model code and software

ToyCTM v1.0 + scripts used to produce the figures in the present study S. Mailler, R. Pennel, L. Menut, and A. Cholakian https://doi.org/10.5281/zenodo.7956919

Sylvain Mailler et al.

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Short summary
We show that a new advection scheme named PPM+W ("Piecewise Parabolic Method + Walcek") offers geoscientific modellers an alternative, high-performance scheme designed for Cartesian-grid advection, with improved performance over the classical PPM scheme. The computational cost of PPM+W is not higher than that of PPM. With improved accuracy and controlled computational cost, this new scheme may find applications in chemistry-transport models, ocean models or atmospheric circulation models.